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September, 1976 Monotone Empirical Bayes Tests for the Continuous One-Parameter Exponential Family
J. C. van Houwelingen
Ann. Statist. 4(5): 981-989 (September, 1976). DOI: 10.1214/aos/1176343596


Let $\theta$ be the natural parameter of a continuous one-parameter exponential family. An empirical Bayes test is constructed for testing $\theta \leqq 0$ against $\theta > 0$ with a piecewise linear loss function. Since the problem is monotone, Bayes tests for a given prior distribution can be characterized by a single parameter, e.g., the size of the test under $\theta = 0$. Therefore the construction of an empirical Bayes test can be reduced to the construction of an estimator of this parameter. Such an estimator is constructed and the convergence rate of its mean squared error is investigated. The empirical Bayes test constructed in this way has not only nice asymptotic properties, but it can also be applied to small samples because of its (weak) admissibility.


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J. C. van Houwelingen. "Monotone Empirical Bayes Tests for the Continuous One-Parameter Exponential Family." Ann. Statist. 4 (5) 981 - 989, September, 1976.


Published: September, 1976
First available in Project Euclid: 12 April 2007

zbMATH: 0339.62002
MathSciNet: MR423623
Digital Object Identifier: 10.1214/aos/1176343596

Primary: 62C10
Secondary: 62F05 , 62F15

Keywords: convergence rate , Empirical Bayes , monotone test

Rights: Copyright © 1976 Institute of Mathematical Statistics

Vol.4 • No. 5 • September, 1976
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